When the pressure on a sample of a dry gas is held constant, the
KelvinKelvin temperature and the volume will be directly related.[1]

This directly proportional relationship can be written as:

V
∝
T

displaystyle Vpropto T

or

V
T

=
k
,

displaystyle frac V T =k,

where:

V is the volume of the gas,
T is the temperature of the gas (measured in kelvins),
k is a constant.

This law describes how a gas expands as the temperature increases;
conversely, a decrease in temperature will lead to a decrease in
volume. For comparing the same substance under two different sets of
conditions, the law can be written as:

The equation shows that, as absolute temperature increases, the volume
of the gas also increases in proportion.

Contents

1 Discovery and naming of the law
2 Relation to absolute zero
3 Relation to kinetic theory
4 See also
5 References
6 Further reading
7 External links

Discovery and naming of the law[edit]
The law was named after scientist Jacques Charles, who formulated the
original law in his unpublished work from the 1780s.
In two of a series of four essays presented between 2 and 30 October
1801,[2]
John DaltonJohn Dalton demonstrated by experiment that all the gases and
vapours that he studied expanded by the same amount between two fixed
points of temperature. The French natural philosopher Joseph Louis
Gay-Lussac confirmed the discovery in a presentation to the French
National Institute on 31 Jan 1802,[3] although he credited the
discovery to unpublished work from the 1780s by Jacques Charles. The
basic principles had already been described by Guillaume Amontons[4]
and Francis Hauksbee[5] a century earlier.
Dalton was the first to demonstrate that the law applied generally to
all gases, and to the vapours of volatile liquids if the temperature
was well above the boiling point. Gay-Lussac concurred.[6] With
measurements only at the two thermometric fixed points of water,
Gay-Lussac was unable to show that the equation relating volume to
temperature was a linear function. On mathematical grounds alone,
Gay-Lussac's paper does not permit the assignment of any law stating
the linear relation. Both Dalton's and Gay-Lussac's main conclusions
can be expressed mathematically as:

V

100

−

V

0

=
k

V

0

displaystyle V_ 100 -V_ 0 =kV_ 0 ,

where V100 is the volume occupied by a given sample of gas at
100 °C; V0 is the volume occupied by the same sample of gas at
0 °C; and k is a constant which is the same for all gases at
constant pressure. This equation does not contain the temperature and
so has nothing to do with what became known as Charles' Law.
Gay-Lussac's value for k (​1⁄2.6666), was identical to Dalton's
earlier value for vapours and remarkably close to the present-day
value of ​1⁄2.7315. Gay-Lussac gave credit for this equation to
unpublished statements by his fellow Republican citizen J. Charles in
1787. In the absence of a firm record, the gas law relating volume to
temperature cannot be named after Charles. Dalton's measurements had
much more scope regarding temperature than Gay-Lussac, not only
measuring the volume at the fixed points of water, but also at two
intermediate points. Unaware of the inaccuracies of mercury
thermometers at the time, which were divided into equal portions
between the fixed points, Dalton, after concluding in Essay II that in
the case of vapours, “any elastic fluid expands nearly in a uniform
manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”,
was unable to confirm it for gases.
Relation to absolute zero[edit]
Charles' law appears to imply that the volume of a gas will descend to
zero at a certain temperature (−266.66 °C according to
Gay-Lussac's figures) or −273.15 °C. Gay-Lussac was clear in
his description that the law was not applicable at low temperatures:

but I may mention that this last conclusion cannot be true except so
long as the compressed vapours remain entirely in the elastic state;
and this requires that their temperature shall be sufficiently
elevated to enable them to resist the pressure which tends to make
them assume the liquid state.[3]

At absolute zero temperature the gas possesses zero amount of energy
and hence the molecules restrict motion. Gay-Lussac had no experience
of liquid air (first prepared in 1877), although he appears to believe
(as did Dalton) that the "permanent gases" such as air and hydrogen
could be liquified. Gay-Lussac had also worked with the vapours of
volatile liquids in demonstrating Charles' law, and was aware that the
law does not apply just above the boiling point of the liquid:

I may however remark that when the temperature of the ether is only a
little above its boiling point, its condensation is a little more
rapid than that of atmospheric air. This fact is related to a
phenomenon which is exhibited by a great many bodies when passing from
the liquid to the solid state, but which is no longer sensible at
temperatures a few degrees above that at which the transition
occurs.[3]

The first mention of a temperature at which the volume of a gas might
descend to zero was by William Thomson (later known as Lord Kelvin) in
1848:[7]

This is what we might anticipate, when we reflect that infinite cold
must correspond to a finite number of degrees of the air-thermometer
below zero; since if we push the strict principle of graduation,
stated above, sufficiently far, we should arrive at a point
corresponding to the volume of air being reduced to nothing, which
would be marked as −273° of the scale (−100/.366, if .366 be the
coefficient of expansion); and therefore −273° of the
air-thermometer is a point which cannot be reached at any finite
temperature, however low.

However, the "absolute zero" on the
KelvinKelvin temperature scale was
originally defined in terms of the second law of thermodynamics, which
Thomson himself described in 1852.[8] Thomson did not assume that this
was equal to the "zero-volume point" of Charles' law, merely that
Charles' law provided the minimum temperature which could be attained.
The two can be shown to be equivalent by Ludwig Boltzmann's
statistical view of entropy (1870).
However, Charles also stated:

The volume of a fixed mass of dry gas increases or decreases by
​1⁄273 times the volume at 0 °C for every 1 °C rise or
fall in temperature. Thus:

V

T

=

V

0

+
(

1
273

×

V

0

)
×
T

displaystyle V_ T =V_ 0 +( tfrac 1 273 times V_ 0 )times T

V

T

=

V

0

(
1
+

T
273

)

displaystyle V_ T =V_ 0 (1+ tfrac T 273 )

where VT is the volume of gas at temperature T, V0 is the volume at
0 °C.

Relation to kinetic theory[edit]
The kinetic theory of gases relates the macroscopic properties of
gases, such as pressure and volume, to the microscopic properties of
the molecules which make up the gas, particularly the mass and speed
of the molecules. In order to derive Charles' law from kinetic theory,
it is necessary to have a microscopic definition of temperature: this
can be conveniently taken as the temperature being proportional to the
average kinetic energy of the gas molecules, Ek:

T
∝

E

k

¯

.

displaystyle Tpropto bar E_ rm k .,

Under this definition, the demonstration of Charles' law is almost
trivial. The kinetic theory equivalent of the ideal gas law relates PV
to the average kinetic energy:

P
V
=

2
3

N

E

k

¯

displaystyle PV= frac 2 3 N bar E_ rm k ,

See also[edit]

Boyle's law
Combined gas law
Gay-Lussac's law
Avogadro's law
Ideal gas law
Hand boiler

Amontons, G. (presented 1699, published 1732) "Moyens de substituer
commodément l'action du feu à la force des hommes et des chevaux
pour mouvoir les machines" (Ways to conveniently substitute the action
of fire for the force of men and horses in order to power machines),
Mémoires de l’Académie des sciences de Paris (presented 1699,
published 1732), 112–126; see especially pages 113–117.
Amontons, G. (presented 1702, published 1743) "Discours sur quelques
propriétés de l'Air, & le moyen d'en connoître la température
dans tous les climats de la Terre" (Discourse on some properties of
air and on the means of knowing the temperature in all climates of the
Earth), Mémoires de l’Académie des sciences de Paris, 155–174.
Review of Amontons' findings: "Sur une nouvelle proprieté de l'air,
et une nouvelle construction de Thermométre" (On a new property of
the air and a new construction of thermometer), Histoire de l'Academie
royale des sciences, 1–8 (submitted: 1702 ; published: 1743).

^

Englishman
Francis HauksbeeFrancis Hauksbee (1660–1713) independently also
discovered Charles' law:
Francis HauksbeeFrancis Hauksbee (1708) "An account of an
experiment touching the different densities of air, from the greatest
natural heat to the greatest natural cold in this climate,"
Philosophical Transactions of the Royal Society of London 26(315):
93–96.